In order to solve constrained optimization problems, a dingo optimization algorithm with ε constrained method and crisscross strategy (εCDOA) was proposed. The algorithm first introduces the crisscross strategy in dingo optimization algorithm after all individuals select one hunting strategy and update their positions, so as to improve the global and local search capabilities of the obtained algorithm, which also help the algorithm jump out of the local optimum. Then, according to ε constrained method, the equality constraints were transformed into the inequality constraints, and the ε level comparison method was used instead of fitness value comparison to evaluate the qualities of the dingoes. Finally, based on the individuals’ constraint violations, the population is divided into two subgroups according to adaptive ε values. The individuals’ survival rates were calculated using the survival strategy of each subgroup, and the individuals with low survival rates were updated. The results of numerical experiments on 19 standard constrained optimization problems in CEC 2006 show that algorithm εCDOA has better optimization performance than four comparative algorithms such as dingo optimization algorithm with ε constrained method. For three classical engineering design problems, the design schemes given by algorithm εCDOA are obviously better than those given by other algorithms.